wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If the equation (a2)(x[x])2+2(x[x])+a2=0,aR has no integral solution and has exactly one solution in [2,3), then a lies in the interval
(where [x] denotes the greatest integer function)

A
(1,2)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
(0,1)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
(1,0)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
(2,3)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C (1,0)
f(x)=(a2)(x[x])2+2(x[x])+a2=0
Let t=x[x]={x}
t[0,1)
(a2)t2+2t+a2=0

It is given that the given equation does not have any integer root.
So t0 ( xZ,x=[x]t=0)
t(0,1)

Case 1: a20
f(t)=(a2)t2+2t+a2=0
For f(x) to have exactly one root in [2,3), f(t) should have exactly one root in the interval (0,1).
f(0)f(1)<0
a2(a2+a)<0
a(1,0)

Case 2: a2=0
Then 2t+a2=0 which is not possible as LHS>0
a(1,0)

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Introduction to Le Chatelier's Principle
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon